The two crossword solutions for the term 'Big Name in Trains' are AMTRAK and Lionel. AMTRAK is a government-owned corporation that provides intercity passenger train service throughout the United States. It was created in 1971 and is the only provider of intercity rail service in the United States. Lionel is a toy train and model railroad company that has been in business since 1900. It is one of the most well-known and respected brands in the model train industry.